I might try cleaning the edge connector on the A500, as well as making sure there aren't any obvious problems in the connector on the A530. The issue may simply be a poor connection. It could certainly give the symptoms you mention.
Beyond that... Well, not a lot you can test without additional hardware or a bit more research. Do you have a voltage tester? Are the power supplies good? I don't remember if the A530 uses Amiga power or has a separate supply. Either way, a power issue is certainly possible, as well, though.
